As a pointer, and a service to other amateur physicists, I thought it would be useful to sum up the main pitfalls and discoveries I stumbled upon while working my way through Feynman’s Lectures. I call it a Survivor’s Guide to Quantum Physics because – at times – it did feel like going through a jungle, or wading through deep water, or climbing a mountain for which there is no map. Indeed, while there is a tendency to present quantum physics as a coherent set of principles and theory, it is not. At best, it is a toolbox with some novel mathematical techniques, approaches and models. At worst, it tries to present itself as an alternative to classical physics, which it is not. Quantum physics is, in essence, a combination of Maxwell’s equations and the Planck-Einstein relation. That is it. Nothing more. Nothing less. In the QED sector, at least. The one and only quantum is Planck’s quantum of (physical) action, and its physical dimension – a force times a distance times a period (cycle time) – is, unfortunately, not always well understood by those who are supposed to understand it – which is why there is a lot of nonsense around. In short, we hope this short paper might help you to avoid the mistakes I made, and that is to waste time on things you should not waste time on: stuff that is not useful, or plain wrong even. And then I will also try to highlight the little shortcuts or visualizations that may help you to get a much more intuitive grasp of things.
As a pointer, and a service to other amateur physicists, I thought it would be useful to sum up the main pitfalls and discoveries I stumbled upon while working my way through Feynman’s Lectures. I call it a Survivor’s Guide to Quantum Physics because – at times – it did feel like going through a jungle, or wading through deep water, or climbing a mountain for which there is no map. Indeed, while there is a tendency to present quantum physics as a coherent set of principles and theory, it is not. At best, it is a toolbox with some novel mathematical techniques, approaches and models. At worst, it tries to present itself as an alternative to classical physics, which it is not. Quantum physics is, in essence, a combination of Maxwell’s equations and the Planck-Einstein relation. That is it. Nothing more. Nothing less. In the QED sector, at least. The one and only quantum is Planck’s quantum of (physical) action, and its physical dimension – a force times a distance times a period (cycle time) – is, unfortunately, not always well understood by those who are supposed to understand it – which is why there is a lot of nonsense around. In short, we hope this short paper might help you to avoid the mistakes I made, and that is to waste time on things you should not waste time on: stuff that is not useful, or plain wrong even. And then I will also try to highlight the little shortcuts or visualizations that may help you to get a much more intuitive grasp of things.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
There are two ways to teach quantum mechanics. The first way – which for most physicists today is still the only way – follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then, you learn about the “blackbody paradox” and various strange experimental results, and the great crisis these things posed for physics. Next, you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study, you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex. Look, obviously the physicists had their reasons for teaching quantum mechanics that way, and it works great for a certain kind of student. But the “historical” approach also has disadvantages, which in the quantum information age are becoming increasingly apparent. For example, I’ve had experts in quantum field theory – people who've spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them , or other simple conceptual things like Grover's algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem.
The relation between Physics and Philosophy brings to mind the proverbial marriage of high drama; the parties do not approve of each other, but separated they cannot live. Philosophers find physicists shallow, and many physicists claim that they find philosophic speculations useless or worse. Mostly both display a lack of knowledge and understanding of the methods and goals of the other. A few researchers have tried to bridge this gap and explore the worlds of both parties. Michael Redhead has worked in this borderland, and when he retired from his chair in Cambridge, a symposium was arranged to honour him. The talks presented on this occasion are now published in a volume presenting much food for thought to both philosophers and physicists. The essays in this publication do not offer easy reading; not too many readers will have the preparation to penetrate the technical arguments offered. The authors are well acquainted with both philosophical argumentation and mathematical formalism, and, following the lead of Professor Redhead, they combine these in intricate and suggestive ways. Only a close reading can offer understanding of the points of view taken by the various authors. Browsing and mere reading defines the scenery, exploring it demands much more. Many of the nine essays included investigate the meaning of terms used loosely in physics contexts: locality, beables, symmetries and time in relativity. All essays utilize the mathematical structures of physics, but the approach is mainly philosophical; concepts like reality and metaphysics are applied. Some writings are more physical in their treatment of technical questions relating to modern quantum theory. Bohmian mechanics, localized quantum states and gauge symmetries are discussed in detail. It is, however, found that these present interpretational problems that are usually glossed over in purely physical treatments. For an old sceptic like myself, it is quite refreshing to find that many assertions, taken for granted in our textbooks, are indeed doubtful and offer conceptual or technical difficulties. This insight is what a philosophical analysis can offer the working physicist; future progress may well arise from such realizations. However, the results offered by philosophical analysis are usually found unsatisfactory; the hope that philosophy can suggest novel directions for the theory remains unfounded. Philosophers can learn that modern physics rests on a very shaky conceptual foundation. The theory has evolved by a combination of serendipity and opportunism. The beast that finally has emerged is neither well founded nor internally consistent. Its only merit is that it works. That offers the ultimate philosophical problem of modern physics. If the present book can help the philosopher to behold this challenging but overwhelming wilderness, then it serves a useful purpose indeed. But the prospective researcher has to learn to master the difficult language used by the natives, who are not always friendly. I enjoyed reading the book immensely, but the technical difficulty of the text made my understanding remain mostly superficial. I hope to have the time to return some of the essays, and look into the references and issues involved. The work is genuinely what it promises: a guide From Physics to Philosophy .
Written at a level appropriate for an educated lay audience, this paper attempts to give a primarily conceptual overview of a framework recently introduced in reference [3] by this author, which attempts to clarify what quantum mechanics tells us about reality. Physicists may find this pa-per useful because it focuses on the central ideas of the framework at a conceptual level, thereby lessening their unfamiliarity, an unavoidable fea-ture of truly novel ideas. The author hopes that this article will motivate physicists to seriously evaluate the mathematical details of the framework given in the original reference...I think I can safely say that nobody understands Quantum Mechanics.”[1]
In 1903 the physicist Albert Michelson made an astonishing pronouncement. Confident of the advances made by the great physicists of the Victorian era, such as Lord Kelvin, James Clark Maxwell and Thomas Edison, he declared that ‘the most important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplemented in consequence of new discoveries is exceedingly remote’.1 In so doing he followed what appeared to be a long-established tradition that eminent physicists should make bold and far-reaching statements on the nature of the universe and its physical laws.2 Unfortunately, Michelson’s timing could not be worse as early twentieth-century physicists were about to make a string of discoveries that would fundamentally alter our perceptions of the universe. The world as Michelson understood it was about to be turned on its head by the work of three men: Max Planck, Albert Einstein and Ernest Rutherford. The first, Planck, was a respected German physicist who had done work on entropy, but had done little to distinguish himself. Then in 1900 he developed his ‘quantum theory’ which posited that energy did not flow as a stream or wave as had been imagined before, but rather was carried by packets or quanta. This seemingly simple, yet deceptively complex, thesis was to have a profound effect upon our understanding of the physical universe. Planck’s thesis proved to be the foundation for the modern discipline of quantum physics, a discipline that first came to the attention of the wider public when in 1905 a young Swiss patents clerk called Albert Einstein wrote five papers for the Annalen der Physik. Three of these papers are widely accepted to be among the best in the history of physics and examined photoelectric effects by applying Planck’s new quantum theory, Brownian Motion and a ‘Special Theory of Relativity’. As Bill Bryson notes in his Short History of Nearly Everything, ‘the first won its author a Nobel Prize and explained the nature of light (and also helped make television possible among other things). The Second provided proof that atoms do indeed exist – a fact that had surprisingly, been in some dispute. The third merely changed the world’.3 Thus within two years of Michelson’s pronouncement much of our understanding of the physical universe had been turned on its head by this new development; but for Michelson worse was to follow. In 1895, a young South African named Ernest Rutherford had won a scholarship to the world famous Cavendish Laboratory at the University of Cambridge. By 1911, Rutherford had become obsessed with the nature of atoms, the basic building blocks that form the constituent parts of the universe. That year he proposed his ‘theory of atomic nuclei’, which suggested that all the positive charge and most of the mass of an atom must be contained in a tiny nucleus at the atom’s centre, with the negatively charged electrons ‘in orbit’ about this nucleus. To prove his thesis Rutherford had to ‘split’ the atom to prove that he could release matter from this nucleus, something which he finally succeeded in doing in 1919 when he showed that by firing alpha-particles into nitrogen gas a small amount of hydrogen could be produced. In so doing he also established that energy could be released from the nucleus of an atom, thereby proving an essential part of Albert Einstein’s Special Theory of Relativity: the unification of energy and mass, usually represented by the famous equation E=mc2.4 With Rutherford providing the link between quantum theory and nuclear physics the Newtonian view of the universe, which was at the heart of Michelson’s beliefs, had been rewritten in less that 20 years.
Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).